document.write( "Question 191409: Two vertices of a triangle in Quadrant 1 are (2,0) and (13,0).The y-coordinate of the third vertex is 2. What is the x-coordinate if the triangle is a right triangle?
\n" ); document.write( "A.2 B.13 C.2 or 13 D.11 or 2 \n" ); document.write( "
Algebra.Com's Answer #143653 by solver91311(24713)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "The two given vertices are on the x-axis. We know that because the y-coordinate of both points is 0. That means one side of the triangle is a horizontal line. So we either have the right angle vertex at either end of the horizontal line, or the right angle at the unspecified vertex.\r
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\n" ); document.write( "\n" ); document.write( "If the right angle is at (2,0), then the adjacent side must be a vertical line and the x-coordinate of ANY point on that vertical line must then be 2. So the point (2,2) is a possibility.\r
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\n" ); document.write( "\n" ); document.write( "A similar argument shows that the point (2,13) is also a possibility. So now we know that answer A, while correct, is definitely NOT the whole story. Likewise answer B. Also, since answer D does not include 13, it doesn't tell the whole story either. Hence, the best answer so far is C.\r
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\n" ); document.write( "\n" ); document.write( "I won't go into it here, but multiple applications of Pythagoras' Theorem can prove conclusively that the point (11, 2) is NOT a right angled vertex with the line segment (2,0) to (13,0) being the hypotenuse. However, there is a point somewhere in the first Quadrant that will form a right triangle with the given segment as the hypotenuse, it is just that the coordinates of that point are not among your selections.\r
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